Diffusion and Laplacian transport
Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 3, pp. 376-388 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study (stationary) Laplacian transport in the Dirichlet-to-Neumann formalism. Our main results concern a formal solution of the geometric inverse problem for localization and the form of absorbing domains. We restrict our analysis to one and two dimensions. We show that the latter case can be studied using the conformal mapping technique.
Keywords: Laplacian transport, Dirichlet-to-Neumann operator
Mots-clés : conformal map.
@article{TMF_2011_168_3_a2,
     author = {I. Baydoun and V. A. Zagrebnov},
     title = {Diffusion and {Laplacian} transport},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {376--388},
     year = {2011},
     volume = {168},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_168_3_a2/}
}
TY  - JOUR
AU  - I. Baydoun
AU  - V. A. Zagrebnov
TI  - Diffusion and Laplacian transport
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2011
SP  - 376
EP  - 388
VL  - 168
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2011_168_3_a2/
LA  - ru
ID  - TMF_2011_168_3_a2
ER  - 
%0 Journal Article
%A I. Baydoun
%A V. A. Zagrebnov
%T Diffusion and Laplacian transport
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2011
%P 376-388
%V 168
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2011_168_3_a2/
%G ru
%F TMF_2011_168_3_a2
I. Baydoun; V. A. Zagrebnov. Diffusion and Laplacian transport. Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 3, pp. 376-388. http://geodesic.mathdoc.fr/item/TMF_2011_168_3_a2/

[1] J. Lee, G. Uhlmann, Comm.Pure Appl. Math., 42:8 (1989), 1097–1112 | DOI | MR | Zbl

[2] D. C. Barber, B. H. Brown, J. Phys. E, 17:9 (1984), 723–733 | DOI

[3] M. E. Taylor, Pseudodifferential Operators, Princeton Univ. Press, Princeton, NJ, 1996 | MR

[4] A. Greenleaf, G. Uhlmann, Duke Math. J., 108 (2001), 559–617 | MR

[5] V. A. Zagrebnov, J. Math. Phys. Anal. Geom., 4:4 (2008), 551–568 | MR | Zbl

[6] B. Sapoval, Phys. Rev. Lett., 73:24 (1994), 3314–3316 | DOI

[7] D. S. Grebenkov, M. Filoche, B. Sapoval, Phys. Rev. E, 73:2 (2006), 021103, 9 pp. | DOI | MR

[8] O.D. Kellogg, Foundations of Potential Theory, Dover, New York, 1954 | MR | Zbl

[9] A. N. Tikhonov, V. Ya. Arsenin, Metody resheniya nekorrektnykh zadach, Nauka, M., 1979 | MR

[10] Jiaqi Liu, Yingwei Lu, “A new algorithm for solving the geometrical inverse problems for a partial differential equation and its numerical semulation”, Proceedings of XI IMACS World Congress on System Simulation and Scientific Computation (Oslo, Norway, 5–9 August 1985), eds. B. Wahlstrom et al., Moberg Helli A/S, Oslo, Norway, 1985, 221–224

[11] A. G. Ramm, Inverse Probl., 2:2 (1986), L19–L21 | DOI | MR | Zbl

[12] M. E. Taylor, Partial Differential Equations II, Appl. Math. Sci., 116, Qualitative Studies of Linear Equations, Springer, New York, 1996 | MR

[13] J. K. Hunter, B. Nachtergaele, Applied Analysis, World Scientific, Singapore, 2001 | MR | Zbl

[14] D. Tataru, Commun. Partial Differ. Equations, 20:5–6 (1995), 855–884 | DOI | MR | Zbl

[15] M. A. Lavrentev, B. V. Shabat, Metody teorii funktsii kompleksnogo peremennogo, Nauka, M., 1987 | MR

[16] S. G. Mikhlin, Kurs matematicheskoi fiziki, Nauka, M., 1968 | MR

[17] I. Baydoun, V. A. Zagrebnov, Localisation of absorbing cells, Preprint Centre de Physique Théorique – HAL (2011), Centre de Physique Théorique UMR 6207, Marseille, 2011